Capacity of Rayleigh fading channels under different adaptive transmissionand diversity-combining techniques

We study the Shannon capacity of adaptive transmission techniques in conjun ction with diversity combining. This capacity provides an upper bound on sp ectral efficiency using these techniques. We obtain closed-form solutions f or the Rayleigh fading channel capacity under three adaptive policies: opti mal power and rate adaptation, constant power with optimal rate adaptation, and channel inversion with fixed rate. Optimal power and rate adaptation y ields a small increase in capacity over just rate adaptation, and this incr ease diminishes as the average received carrier-to-noise ratio (CNR) or the number of diversity branches increases, Channel inversion suffers the larg est capacity penalty relative to the optimal technique, however, the penalt y diminishes with increased diversity. Although diversity yields large capa city gains for all the techniques, the gain is most pronounced with channel inversion. For example, the capacity using channel inversion with two-bran ch diversity exceeds that of a single-branch system using optimal rate and power adaptation. Since channel inversion is the least complex scheme to im plement, there is a tradeoff between complexity and capacity for the variou s adaptation methods and diversity-combining techniques.